Abstract:

In order to study the influence of the strength of geometric nonlinearity on the applicability of Galerkin discretization method under the background of single horizontal cable. Two kinds of different non-dimensional parameters are introduced to dimensionless the nonlinear equations of motion in the cable plane, and it was transformed into an ordinary differential equation using Galerkin method. Using the method of multiple scale to get perturbation solution, the corresponding frequency response equations are derived, and draw the amplitude-frequency response curve; Then MATLAB is used to obtain the time history curve of the system. Finally, ABAQUS software is used to carry out finite element simulation, and the results are compared with the numerical solutions of the method. While the time history curve of the system is obtained by numerical simulation, the two dimensionless methods are also compared. The results show that the Galerkin discrete method is more suitable for systems with weak geometric non-linearity. Dimensionless will lead to the increase of the nonlinear term coefficient of the system. system.The?numerical?solutions?obtained?by?the?two?dimensionless?methods?are?more?similar?with?the?increase?of?Irvine?coefficient. The research results may provide a basis for the numerical solution of nonlinear vibration of cables and contribute to the perfection of the theory.

摘要：

为研究单跨水平拉索背景下几何非线性的强弱对Galerkin离散法适用性产生的影响,首先引入两种不同的无量纲参数，将拉索面内非线性运动方程无量纲化，运用Galerkin离散法将偏微分运动方程转化为常微分方程，利用多尺度法进行摄动求解，得到幅频响应函数，并绘制幅频响应曲线；接着应用MATLAB得出系统时间历程曲线，最后应用ABAQUS软件进行有限元模拟，将有限元解与本文方法计算得到的数值解进行对比。在通过数值模拟得到系统时间历程曲线的同时，将两种无量纲方法也进行对比。结果表明：Galerkin离散法对于几何非线性较弱的系统适用性较高。无量纲化会导致系统非线性项系数变大。两种无量纲方法随着Irvine系数的增大，所得数值解更接近。研究成果可为索的非线性振动数值求解提供依据且有助于理论的完善。

关键词: 振动与波, 拉索, 模态分析, 有限元, 离散法, 无量纲化